You can use heavy clear vinyl if you need something flexible, so long as you design the rigging properly to handle the torsional forces of the wings. But I agree with Penlowe. The fleshtoned technique tends to look much better, particularly when blended well with makeup.
What material you need beneath the spandex is dependent on the design of your wings, your costume, and your harness. There are a number of techniques; some involve a rigid harness, and some use flexible strapping.
As far as sewing, you can sew almost anything to anything. The trick is just to predrill or prepunch the required holes, and then sew it on using an appropriate hand sewing stitch (I tend to use the classic saddle stitch due to my leather background). One secure pattern to use for the holes is the box with an 'X' through it. You'll commonly see this pattern used to secure bookbag straps in place.
Originally Posted by StabbityBlkMage
So yeah I primarily work with clear acrylic, but others have been pushing me to plexi.
"Plexiglass" is a brand name for acrylic sheet (aka Poly methyl-methacrylate). They're the same thing. The common alternative is the stronger, but more expensive "polycarbonate", aka "Lexan".